Standard statistical methods applied to general time series might not work.

Cointegration extends regression methods to cover more cases.

I'll talk about implementation of solution methods.

I(0) time series are formally expressed

A series x_t is called I(1) if

The I(1) vector x_t is cointegrated if there exists a vector β such that

The I(1) series x_t has cointegration rank 1 if

Require each series to be I(1).

^{α, β full column rank}